Moura, Scott. 2016. Chapter 1: Modeling ad Systems Analysis. Class Notes for CE 295 — Energy Systems and Control, University of California, Berkeley. 20 pp.
Overview: The fundamental step in performing systems analysis and control design in energy systems is mathematical modeling. That is, we seek to write the ordinary differential equations (ODEs) that describe the physics of the particular energy system of interest. This process is highly non-trivial, and requires a careful combination of first principles (e.g. physics, chemistry, thermodynamics), experience, and creativity. Once these equations are properly derived, we then formulate the system dynamics into a so-called “state-space” form. The state-space form is the canonical template for analysis and control. State-space models can be divided into linear and nonlinear systems. We next focus on linear systems, and how they can be derived from nonlinear systems. The next and final fundamental concept is “stability”. Stability, in rough terms, means the energy system does not “blow up” in some sense. In summary, this chapter is organized as follows:
1. Mathematical modeling of dynamic systems
2. State-space representations
3. Linear Systems
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